• 대한수학회지
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• 제38권3호
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• pp.645-656
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• 2001

In this paper, we will prove the Hyers-Ulam stability of the quadratic functional equation of Pexider type, f$_1$(x+y) + F$_2$(x-y) = f$_3$(x) + f$_4$(y).

• Nonlinear Functional Analysis and Applications
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• 제28권1호
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• pp.95-105
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• 2023

In the present paper, we introduce a new system of functional equations, known as orthogonal Pexider hom-derivation and Pexider hom-Pexider derivation (briefly, (Pexider) hom-derivation). Using the fixed point method, we investigate the stability of Pexider hom-derivations and (Pexider) hom-derivations on Banach algebras.

• 호남수학학술지
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• 제27권3호
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• pp.421-429
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• 2005

Generalizing the results in [7] that considers several functional equations in the spaces of the Schwartz tempered distributions and the Fourier hyperfunctions we consider Pexider type functional equations in the space of distributions.

• Korean Journal of Mathematics
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• 제16권3호
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• pp.369-378
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• 2008

The aim of this paper is to study the stability problem for the pexider type trigonometric functional equation f(x + y) − f(x−y) = 2g(x)h(y), which is related to the d'Alembert, the Wilson, the sine, and the mixed trigonometric functional equations.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권1호
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• pp.51-60
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• 2020

In this note, we investigate the Hyers-Ulam stability and the hyperstability of the Pexider type functional equation g(x + y + xy) = g(x) + f(y) + xf(y) + yg(x).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제17권4호
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• pp.397-411
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• 2010

In this paper, we will investigate the superstability for the sine functional equation from the following Pexider type functional equation: $f(x+y)-g(x-y)={\lambda}{\cdot}h(x)k(y)$ ${\lambda}$: constant, which can be considered an exponential type functional equation, the mixed functional equation of the trigonometric function, the mixed functional equation of the hyperbolic function, and the Jensen type equation.

• 대한수학회지
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• 제41권3호
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• pp.501-511
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• 2004

We prove the Hyers-Ulam-Rassias stability of the Davison functional equation f($\chi$y) + f($\chi$ + y) = f($\chi$y + $\chi$) + f(y) for a class of functions from a ring into a Banach space and we also investigate the Davison equation of Pexider type.

• 대한수학회지
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• 제37권1호
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• pp.111-124
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• 2000

In this paper we obtain the Hyers-Ulam-Rassias stability of the Pexider equation f(x+y) =g(x)+h(y) in the spirit of Hyers, Ulam, Rassias and Gavruta.

• 충청수학회지
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• 제25권1호
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• pp.1-18
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• 2012

The aim of this paper is to investigate the superstability of the pexider type sine(hyperbolic sine) functional equation $f(\frac{x+y}{2})^{2}-f(\frac{x+{\sigma}y}{2})^{2}={\lambda}g(x)h(y),\;{\lambda}:\;constant$ which is bounded by the unknown functions ${\varphi}(x)$ or ${\varphi}(y)$. As a consequence, we have generalized the stability results for the sine functional equation by P. M. Cholewa, R. Badora, R. Ger, and G. H. Kim.

• Korean Journal of Mathematics
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• 제20권2호
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• pp.213-223
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• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.